Superannuation (1 Viewer)

[.ben]

2 John and Sally were married recently and wanted to buy a house around $80000. They planned to save for five
for a good deposit for one of those houses.
a) If they can deposit $400 per month to an account paying 15% p.a., how much can they withdraw in 5 years ?


thanks

 

[SoulSearcher]

Ok, what you do here is try to establish a geometric series from the information that you have been given. The rate will be 0.15/12 + 1 = 1.0125
For the first month, assuming they will pay the interest at the end of the month, and that each of the $400 is paid at the beginning of the month,
A₁ = 400
A₂ = 400 * 1.0125 + 400
A₃ = (400 * 1.0125 + 400) * 1.0125 + 400
= 400[ 1.0125² + 1.0125 + 1 ]
A₄ = 400[ 1.0125² + 1.0125 + 1 ] * 1.0125 + 400
= 400 [ 1.0125³ + 1.0125² + 1.0125 + 1 ]
and so on, until you reach the end of the 60 months, after the interest is paid, and before they pay $400 into the account,
A₆₁ = 400[ 1.0125⁶⁰ + 1.0125⁵⁹ + ... + 1.0125 + 1]
= 400 * { 1.0125(1.0125⁶⁰ - 1) / (1.0125 - 1) }
which should equal $35, 872. 68
Please correct me if I am wrong, haven't done these types of questions for a while.